Question

The probability of a boy student getting scholarship is $0.90$ and that of a girl student getting scholarship is $0.80$. The probability that none getting any scholarship is:

• A. $\frac{98}{100}$
• B. $\frac{2}{100}$
• C. $\frac{72}{100}$
• D. $\frac{28}{100}$

Answer 1

Answer: (B)

$\frac{2}{100}$

Given the probability that a boy student will get the scholarship is $P\left(A\right)=0.90$

and, the probability that a girl student will get the scholarship is $P\left(B\right)=0.80$

Hence, the probability that none of them get the scholarship is $1-\left(P\right(A)+P(B)-(P\left(A\right)\times P\left(B\right)\left)\right)=1-(0.9+0.8-(0.8\times 0.9\left)\right)$

$=1-(1.7-0.72)=1-0.98=0.02=\frac{2}{100}$